A scientist is interested in two different types of particles; type A and type B. The time that it takes a particle of type A to decay can be modeled as an exponential distribution with a mean of 75 minutes, and the time that it takes for a particle of type B to decay can be modeled as an exponential distribution with a mean of 50 minutes. Suppose that a container holds 10 particles; 7 of type A and 3 of type B. Assume that the rate at which each of the particles decays is independent of all of the other particles in the container. (1) Calculate the probability that the first particle to decay is of type A. (2) Calculate the probability of the following event; "it takes at least 30 minutes for any of the particles to decay, and the first particle that decays is of type B".
A scientist is interested in two different types of particles; type A and type B. The time that it takes a particle of type A to decay can be modeled as an exponential distribution with a mean of 75 minutes, and the time that it takes for a particle of type B to decay can be modeled as an exponential distribution with a mean of 50 minutes. Suppose that a container holds 10 particles; 7 of type A and 3 of type B. Assume that the rate at which each of the particles decays is independent of all of the other particles in the container. (1) Calculate the probability that the first particle to decay is of type A. (2) Calculate the probability of the following event; "it takes at least 30 minutes for any of the particles to decay, and the first particle that decays is of type B".
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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Transcribed Image Text:A scientist is interested in two different types of particles; type A and type B. The time that it takes for
a particle of type A to decay can be modeled as an exponential distribution with a mean of 75
minutes, and the time that it takes for a particle of type B to decay can be modeled as an
exponential distribution with a mean of 50 minutes.
Suppose that a container holds 10 particles; 7 of type A and 3 of type B. Assume that the rate at
which each of the particles decays is independent of all of the other particles in the container.
(1) Calculate the probability that the first particle to decay is of type A.
(2) Calculate the probability of the following event; "it takes at least 30 minutes for any of the
particles to decay, and the first particle that decays is of type B".
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